Weber-Schafheitlin-type integrals with exponent 1.(English)Zbl 1163.33313

Authors’ abstract: Explicit formulae for Weber-Schafheitlin-type integrals with exponent 1 are derived. The results of these integrals are distributions on $$\mathbb R_{+}$$.

MSC:

 33C55 Spherical harmonics 33D15 Basic hypergeometric functions in one variable, $${}_r\phi_s$$
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References:

 [1] Abramowitz M., National Bureau of Standards Applied Mathematics Series 55 (1964) [2] Da\c{}browski L., J. Math. Phys. 39 pp 47– (1998) · Zbl 0916.47053 [3] Gradshteyn I. S., Table of Integrals, Series, and Products (1965) · Zbl 0918.65002 [4] Miller A. R., J. Comput. Appl. Math. 85 pp 271– (1997) · Zbl 0889.44004 [5] Miller A. R., J. Comput. Appl. Math. 118 pp 301– (2000) · Zbl 1015.33004 [6] Miller A. R., J. Comput. Appl. Math. 137 pp 77– (2001) · Zbl 0992.44001 [7] DOI: 10.1017/S0334270000012480 · Zbl 0915.33006 [8] Miroshin R. N., Math. Notes 70 pp 682– (2001) · Zbl 1023.33016 [9] Srivastava H. M., J. Reine Angew. Math. 309 pp 1– (1979) [10] Watson G. N., A Treatise on the Theory of Bessel Functions, 2. ed. (1966) · Zbl 0174.36202 [11] Wheelon A. D., Tables of Summable Series and Integrals Involving Bessel Functions (1968) · Zbl 0187.12901
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